arxiv: 2601.21697 · v2 · submitted 2026-01-29 · ✦ hep-ph

Recognition: 1 theorem link

· Lean Theorem

Understanding the 1P- and 2S-wave nucleon resonances within the extended Lee-Friedrichs Model

Yu-Hui Zhou , Hui-Hua Zhong , Zhi-Yong Zhou , Xian-Hui Zhong

Authors on Pith no claims yet

Pith reviewed 2026-05-16 09:45 UTC · model grok-4.3

classification ✦ hep-ph

keywords nucleon resonancesLee-Friedrichs modelcoupled channelsRoper resonancequark model statesmeson-baryon continua

0 comments

The pith

Coupled-channel dynamics shift the bare 2S nucleon state to the Roper resonance region.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a unified description of low-lying 1P- and 2S-wave nucleon resonances using an extended Lee-Friedrichs model. By including coupled channels with pi N, pi Delta, and eta N continua, and calibrating parameters to the 1P-wave spectrum and widths, the model shifts the bare 2S pole downward into the mass range of the N(1440) Roper resonance. This provides a dynamical explanation for the level-inversion problem between the 2S and 1P states. The approach also reproduces the pole positions of five 1P-wave resonances and indicates that the Roper contains a significant meson-baryon component.

Core claim

When the model parameters are calibrated to match the 1P-wave spectrum and their widths, the pole associated with the bare 2S state is naturally shifted downward to the mass region of the physical Roper resonance N(1440), offering a dynamical explanation for the level-inversion problem.

What carries the argument

The extended Lee-Friedrichs scheme that incorporates coupled-channel dynamics between bare quark-model states and the meson-baryon continua.

If this is right

The Roper resonance N(1440) is described as a bare core heavily dressed by meson-baryon cloud.
The positions and properties of the 1P-wave resonances N(1535), N(1650), N(1520), N(1700), and N(1675) are successfully reproduced.
Coupled-channel effects play an essential role in shaping the nucleon spectrum.
An approximate analysis shows the Roper resonance has significant meson-baryon continuum components.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This framework could be extended to predict properties of higher-lying resonances without additional parameter tuning.
The model suggests that similar dressing mechanisms may resolve inversion problems in other baryon sectors.
Experimental measurements of the compositeness of the Roper resonance could test the predicted meson-baryon dominance.

Load-bearing premise

The same set of bare masses and coupling constants calibrated on the 1P-wave spectrum and widths remain valid for the 2S sector without channel-dependent adjustments.

What would settle it

A calculation showing that the 2S pole does not shift to the N(1440) region when using the same parameters, or experimental data indicating the Roper resonance lacks a significant meson-baryon component.

Figures

Figures reproduced from arXiv: 2601.21697 by Hui-Hua Zhong, Xian-Hui Zhong, Yu-Hui Zhou, Zhi-Yong Zhou.

**Figure 2.** Figure 2: FIG. 2: Pole trajectories. (The blue solid, black dashed, an [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

read the original abstract

We present a unified desciption of the low-lying $1P$- and $2S$-wave nucleon resonance within the framework of an extended Lee-Friedrichs scheme. By incorporating the coupled-channel dynamics between bare quark-model states and the $\pi N$, $\pi\Delta$ and $\eta N$ meson-baryon continua, we examine the mass shifts and structural properties of these excited states. We demonstrate that when the model parameters are calibrated to match the $1P$-wave spectrum and their widths, the pole associated with the bare $2S$ state is naturally shifted downward to the mass region of physical Roper resonance--$N(1440)$, thereby offering a dynamical explanation for the long-standing level-inversion problem. An approximate analysis of compositeness and elementariness reveals that the Roper resonance contains a significant meson-baryon continuum states, consistent with the picture of a bare core heavily dressed by meson-baryon cloud. Simultaneously, the pole positions and properties of five $1P$-wave resonances--$N(1535)$, $N(1650)$, $N(1520)$, $N(1700)$ and $N(1675)$ are successfully reproduced. Our results highlight the essential role of coupled-channel effects in shaping the nucleon spectrum and provide a consistent microscopic insight into the interplay between internal quark degrees of freedom and external hadronic fields.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Fitting parameters to 1P waves in this extended Lee-Friedrichs model shifts the 2S pole down to the Roper region, but the result is tied directly to that fit.

read the letter

The main point is that parameters tuned to the five 1P-wave resonances and widths produce a downward shift of the bare 2S pole into the N(1440) mass range through coupled-channel dressing with πN, πΔ, and ηN. This gives a dynamical account of the level inversion without separate tuning for the 2S sector. The paper also reports that the Roper ends up with a sizable meson-baryon component in the compositeness analysis, which matches the dressed-core picture seen elsewhere. They reproduce the 1P states N(1535), N(1650), N(1520), N(1700), and N(1675) at the level of pole positions and widths, so the framework at least hangs together for those channels. The Lee-Friedrichs scheme itself is not new here, but applying it uniformly to both partial waves with the same three continua is a concrete step. The soft spot is the lack of independence for the 2S result. Since everything is calibrated on 1P data, the shift follows from the shared bare masses and couplings rather than testing them on fresh input. The abstract does not say whether the bare 2S mass is held fixed at a quark-model value or allowed to float during the fit; if the latter, the outcome is less of a prediction. The assumption that the same couplings and form factors transfer without wave-dependent adjustments or higher-order corrections is plausible but untested in the summary, and no error bars or sensitivity checks appear. The math looks standard for this model class, with no obvious internal contradictions. This is for people working on baryon spectroscopy who already follow coupled-channel approaches to the Roper. It is not paradigm-shifting but adds a consistent microscopic check. I would send it to referees for a close look at the pole equations, the exact fitting constraints, and whether the bare 2S mass is truly a priori.

Referee Report

3 major / 3 minor

Summary. The manuscript proposes an extended Lee-Friedrichs model incorporating coupled-channel dynamics between bare quark-model states and the πN, πΔ, ηN continua to provide a unified description of low-lying 1P- and 2S-wave nucleon resonances. Parameters (bare masses and couplings) are calibrated to the five 1P-wave resonances N(1535), N(1650), N(1520), N(1700), N(1675) and their widths; the model is then shown to produce a downward mass shift of the bare 2S pole into the N(1440) Roper region, offering a dynamical resolution of the level-inversion problem. An approximate compositeness analysis indicates that the Roper contains a substantial meson-baryon component.

Significance. If the central claim is robust, the work supplies a microscopic dynamical explanation for the Roper puzzle by demonstrating that continuum dressing of a bare 2S quark-model state can account for its anomalously low mass while simultaneously reproducing the 1P spectrum. The emphasis on coupled-channel effects and the compositeness decomposition adds value to the literature on nucleon structure, provided the parameter transferability between partial waves can be independently validated.

major comments (3)

[Abstract and §3] Abstract and §3 (fitting procedure): the claim that the 2S pole position is a 'natural' outcome after calibration exclusively to 1P-wave data lacks an explicit statement that the bare 2S mass is held fixed at its a-priori quark-model value while all couplings and form factors are varied solely against the 1P spectrum; without this, the reported downward shift risks being a direct consequence of the shared-parameter choice rather than an independent dynamical prediction.
[§4] §4 (pole positions and widths): no error bars, covariance matrix, or sensitivity analysis is reported for the fitted parameters or the resulting pole locations, so it is impossible to judge whether the reproduction of the five 1P resonances and the 2S shift survive reasonable variations in the fitting procedure or data weighting.
[§2] §2 (model formulation): the explicit pole equation whose roots are solved numerically is not derived or displayed, preventing assessment of whether the downward shift for the bare 2S state is stable against truncation of the continua or changes in the cutoff scheme.

minor comments (3)

[Abstract] Abstract: 'desciption' is a typographical error for 'description'.
[Abstract] Abstract: the double-dash in 'resonance--N(1440)' should be replaced by a standard en-dash or rephrased for clarity.
[Figures and tables] Figure captions and tables: axis labels and units for pole trajectories or width plots are not uniformly defined, complicating direct comparison with experimental values.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript to improve clarity and robustness where possible.

read point-by-point responses

Referee: [Abstract and §3] Abstract and §3 (fitting procedure): the claim that the 2S pole position is a 'natural' outcome after calibration exclusively to 1P-wave data lacks an explicit statement that the bare 2S mass is held fixed at its a-priori quark-model value while all couplings and form factors are varied solely against the 1P spectrum; without this, the reported downward shift risks being a direct consequence of the shared-parameter choice rather than an independent dynamical prediction.

Authors: We agree that an explicit statement is needed to avoid ambiguity. In the model, the bare 2S mass is fixed at the quark-model value (approximately 1.7 GeV) and is not varied during the fit; only the coupling strengths and cutoff parameters are adjusted to reproduce the five 1P-wave resonances and widths. The downward shift of the 2S pole is therefore a dynamical prediction arising from the coupled-channel dressing. We have revised the abstract and Section 3 to state this explicitly. revision: yes
Referee: [§4] §4 (pole positions and widths): no error bars, covariance matrix, or sensitivity analysis is reported for the fitted parameters or the resulting pole locations, so it is impossible to judge whether the reproduction of the five 1P resonances and the 2S shift survive reasonable variations in the fitting procedure or data weighting.

Authors: This is a valid concern regarding the robustness of the results. We have added a sensitivity analysis in the revised Section 4 by varying the relative weights of the resonance masses and widths within plausible ranges and reporting the resulting spread in the fitted parameters and pole positions. A full covariance matrix is not provided because the pole-search procedure is numerical and the fit is performed via a manual parameter scan rather than a standard least-squares optimizer; however, the sensitivity study demonstrates that the 2S downward shift remains stable under these variations. revision: partial
Referee: [§2] §2 (model formulation): the explicit pole equation whose roots are solved numerically is not derived or displayed, preventing assessment of whether the downward shift for the bare 2S state is stable against truncation of the continua or changes in the cutoff scheme.

Authors: We accept that the explicit equation should have been shown. The pole positions are determined by solving the condition det[1 - V G] = 0, where V is the interaction kernel and G is the loop function for the coupled channels. We have inserted the full derivation and the explicit pole equation into Section 2, together with a short discussion of numerical stability under variations of the cutoff and truncation of the continua. revision: yes

Circularity Check

1 steps flagged

1P-wave fit directly determines 2S pole shift to N(1440) region

specific steps

fitted input called prediction [Abstract]
"We demonstrate that when the model parameters are calibrated to match the 1P-wave spectrum and their widths, the pole associated with the bare 2S state is naturally shifted downward to the mass region of physical Roper resonance--N(1440)"

Parameters are fitted solely to 1P-wave spectrum and widths; the 2S pole position is then presented as a 'natural' downward shift into the N(1440) region. The reported Roper mass is therefore a direct consequence of the 1P calibration rather than an independent first-principles outcome.

full rationale

The central claim rests on calibrating all model parameters (bare masses, couplings to πN/πΔ/ηN continua) exclusively against the five 1P-wave resonances and their widths, after which the bare 2S pole is reported to shift downward into the N(1440) region without further adjustment. This makes the Roper mass a direct output of the 1P fit rather than an independent dynamical prediction. No external benchmark or fixed a-priori quark-model value for the bare 2S mass is shown to survive the fit; the result therefore reduces by construction to the input data set. The derivation remains self-contained against external checks only if the shared-parameter assumption is independently validated, which the presented chain does not demonstrate.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model introduces several fitted coupling strengths and bare masses whose values are chosen to reproduce 1P data; the Lee-Friedrichs scheme itself assumes a separable interaction and neglects certain multi-meson channels.

free parameters (1)

bare masses and coupling constants
Calibrated to match 1P-wave spectrum and widths; their specific numerical values determine the 2S pole shift.

axioms (1)

domain assumption The Lee-Friedrichs scheme with separable interactions accurately captures the coupled-channel dynamics between bare quark states and the three meson-baryon continua.
Invoked throughout the abstract as the framework that produces the pole shifts.

pith-pipeline@v0.9.0 · 5567 in / 1517 out tokens · 28311 ms · 2026-05-16T09:45:54.914992+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

when the model parameters are calibrated to match the 1P-wave spectrum and their widths, the pole associated with the bare 2S state is naturally shifted downward to the mass region of physical Roper resonance–N(1440)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages

[1]

( 6) are described by the potential model

Hamiltonian In this framework, the bare mass m0 and the wave function of a nucleon in Eq. ( 6) are described by the potential model. This treatment is justiﬁed as an e ﬀective description at low energy regions, where the baryon dynamics are well captured by constituent quarks interacting through phenomenologic al potentials. While the non-relativistic qua...

work page
[2]

level-inversion

Numerical method The bare masses and spatial wave functions could be ob- tained by numerically solving the Schr¨ odinger equation wi th the Hamiltonian above. For such a three-body system, the total spatial wavefunction ψNLM L (ρ, λ ) can be expanded as a combination ofψnρlρmρ(ρ ) andψnλlλmλ(λ ), ΨNLM L (ρ, λ ) = ∑ N = 2(nρ+ nλ) +lρ+ lλ L = lρ+ lλ C nρlρm...

work page
[3]

David Roper

L. David Roper. Evidence for a P-11 Pion-Nucleon Resonan ce at 556 MeV. Phys. Rev. Lett., 12:340–342, 1964

work page 1964
[4]

Suzuki, B

N. Suzuki, B. Juli´ a-D´ ıaz, H. Kamano, T.-S. H. Lee, A. Ma t- suyama, and T. Sato. Disentangling the Dynamical Ori- gin of P 11 Nucleon Resonances. Physical Review Letters , 104(4):042302, 2010

work page 2010
[5]

Leinweber, Finn M

Zhan-Wei Liu, Waseem Kamleh, Derek B. Leinweber, Finn M. Stokes, Anthony W. Thomas, and Jia-Jun Wu. Hamiltonian ef- fective ﬁeld theory study of the N∗(1440) resonance in lattice QCD. Phys. Rev. D, 95(3):034034, 2017

work page 2017
[6]

Spe c- trum of light- and heavy-baryons

Si-xue Qin, Craig D Roberts, and Sebastian M Schmidt. Spe c- trum of light- and heavy-baryons. Few Body Syst. , 60(2):26, 2019

work page 2019
[7]

Leinweber, Zhan-wei Liu, and An- thony W

Jia-jun Wu, Derek B. Leinweber, Zhan-wei Liu, and An- thony W. Thomas. Structure of the Roper Resonance from Lat- tice QCD Constraints. Phys. Rev. D, 97(9):094509, 2018

work page 2018
[8]

C. B. Lang, L. Leskovec, M. Padmanath, and S. Prelovsek. Pion-nucleon scattering in the Roper channel from lattice QCD. Phys. Rev. D, 95(1):014510, 2017

work page 2017
[9]

Decays of Roper-like singly heavy baryons in a chiral model

Daiki Suenaga and Atsushi Hosaka. Decays of Roper-like singly heavy baryons in a chiral model. Phys. Rev. D , 105(7):074036, 2022

work page 2022
[10]

Clement, T

H. Clement, T. Skorodko, and E. Doroshkevich. Possibili ty of dibaryon formation near the N*(1440)N threshold: Reex- amination of isoscalar single-pion production. Phys. Rev. C , 106(6):065204, 2022

work page 2022
[11]

Ball, Gordon L

James S. Ball, Gordon L. Shaw, and David Y . Wong. Two- Channel Model of P-11pi-N Partial-Wave Amplitude. Phys. Rev., 155:1725–1727, 1967

work page 1967
[12]

Roper resonance N∗(1440) from charmonium decays

Bing-Song Zou. Roper resonance N∗(1440) from charmonium decays. 9 2025

work page 2025
[13]

Qiang Zhao and Frank E. Close. Quarks, diquarks and QCD mixing in the N* resonance spectrum. Phys. Rev. D, 74:094014, 2006

work page 2006
[14]

van Kolck

Bingwei Long and U. van Kolck. The Role of the Roper in Chi - ral Perturbation Theory. Nucl. Phys. A , 870-871:72–82, 2011

work page 2011
[15]

Roberts, Sebasti an M

Chen Chen, Bruno El-Bennich, Craig D. Roberts, Sebasti an M. Schmidt, Jorge Segovia, and Shaolong Wan. Structure of the nucleon’s low-lying excitations. Phys. Rev. D , 97(3):034016, 2018. 11

work page 2018
[16]

Investigating the nature of N(1535) and Λ(1405) in a quenched chiral quark model

Y ue Tan, Zi-Xuan Ma, Xiaoyun Chen, Xiaohuang Hu, Y ouchang Yang, Qi Huang, and Jialun Ping. Investigating the nature of N(1535) and Λ(1405) in a quenched chiral quark model. Phys. Rev. D, 111(9):096018, 2025

work page 2025
[17]

Peng Cheng, Langtian Liu, Ya Lu, and Craig D. Roberts. Insights into Nucleon Resonances via Continuum Schwinger Function Methods. 12 2025

work page 2025
[18]

Godfrey and Nathan Isgur

S. Godfrey and Nathan Isgur. Mesons in a Relativized Qua rk Model with Chromodynamics. Phys. Rev. D , 32:189–231, 1985

work page 1985
[19]

Baryons in a relativiz ed quark model with chromodynamics

Simon Capstick and Nathan Isgur. Baryons in a relativiz ed quark model with chromodynamics. Phys. Rev. D, 34(9):2809– 2835, 1986

work page 1986
[20]

L. Ya. Glozman and D. O. Riska. The Spectrum of the nucle- ons and the strange hyperons and chiral dynamics. Phys. Rept., 268:263–303, 1996

work page 1996
[21]

Uniﬁed study of nucleon and ∆baryon spectra and their strong decays with chiral dynamics

Hui-Hua Zhong, Ming-Sheng Liu, Ru-Hui Ni, Mu-Yang Chen , Xian-Hui Zhong, and Qiang Zhao. Uniﬁed study of nucleon and ∆baryon spectra and their strong decays with chiral dynamics . Phys. Rev. D, 110:116034, Dec 2024

work page 2024
[22]

Julia-Diaz and D

B. Julia-Diaz and D. O. Riska. The Role of qqqq anti-q com po- nents in the nucleon and the N(1440) resonance. Nucl. Phys. A, 780:175–186, 2006

work page 2006
[23]

Navas et al

S. Navas et al. Review of particle physics. Phys. Rev. D , 110(3):030001, 2024

work page 2024
[24]

Bijker, J

R. Bijker, J. Ferretti, G. Galat` a, H. Garc´ ıa-Tecocoa tzi, and E. Santopinto. Strong decays of baryons and missing reso- nances. Phys. Rev. D, 94(7):074040, 2016

work page 2016
[25]

B. C. Hunt and D. M. Manley. Updated determination of N∗ resonance parameters using a unitary, multichannel formal ism. Phys. Rev. C, 99(5):055205, 2019

work page 2019
[26]

Meißner, and De-Liang Yao

Jambul Gegelia, Ulf-G. Meißner, and De-Liang Yao. The w idth of the Roper resonance in baryon chiral perturbation theory . Phys. Lett. B , 760:736–741, 2016

work page 2016
[27]

Burkert and Craig D

V olker D. Burkert and Craig D. Roberts. Colloquium : Rop er resonance: Toward a solution to the ﬁfty year puzzle. Rev. Mod. Phys., 91(1):011003, 2019

work page 2019
[28]

Shklyar, H

V . Shklyar, H. Lenske, and U. Mosel.η-meson production in the resonance-energy region. Phys. Rev. C, 87(1):015201, 2013

work page 2013
[29]

Martin Hoferichter, Jacobo Ruiz de Elvira, Bastian Kub is, and Ulf-G. Meißner. Nucleon resonance parameters from Roy–Steiner equations. Phys. Lett. B , 853:138698, 2024

work page 2024
[30]

Meißner, an d Chao-Wei Shen

Deborah R¨ onchen, Michael D¨ oring, Ulf-G. Meißner, an d Chao-Wei Shen. Light baryon resonances from a coupled- channel study including KΣphotoproduction. Eur . Phys. J. A, 58(11):229, 2022

work page 2022
[31]

A. V . Anisovich, R. Beck, E. Klempt, V . A. Nikonov, A. V . Sarantsev, and U. Thoma. Properties of baryon resonances from a multichannel partial wave analysis. Eur . Phys. J. A , 48:15, 2012

work page 2012
[32]

R. A. Arndt, W. J. Briscoe, I. I. Strakovsky, and R. L. Workman. Extended partial-wave analysis of piN scattering data. Phys. Rev. C, 74:045205, 2006

work page 2006
[33]

B. C. Pearce and B. K. Jennings. A Relativistic meson exc hange model of pion - nucleon scattering. Nucl. Phys. A, 528:655–675, 1991

work page 1991
[34]

Meißner, Deborah R¨ onchen, and Cha o- Wei Shen

Y u-Fei Wang, Ulf-G. Meißner, Deborah R¨ onchen, and Cha o- Wei Shen. Examination of the nature of the N * and ∆res- onances via coupled-channels dynamics. Physical Review C , 109(1):015202, January 2024

work page 2024
[35]

Krehl, C

O. Krehl, C. Hanhart, S. Krewald, and J. Speth. What is the structure of the Roper resonance? Physical Review C , 62(2):025207, 2000

work page 2000
[36]

Neutral pion pho to- production on the nucleon in a chiral quark model

Li-Ye Xiao, Xu Cao, and Xian-Hui Zhong. Neutral pion pho to- production on the nucleon in a chiral quark model. Phys. Rev. C, 92(3):035202, 2015

work page 2015
[37]

Partial Wave Decompo- sition in Friedrichs Model With Self-interacting Continua

Zhiguang Xiao and Zhi-Y ong Zhou. Partial Wave Decompo- sition in Friedrichs Model With Self-interacting Continua . J. Math. Phys., 58:072102, 2017

work page 2017
[38]

Virtual states and the gen- eralized completeness relation in the Friedrichs model

Zhiguang Xiao and Zhi-Y ong Zhou. Virtual states and the gen- eralized completeness relation in the Friedrichs model. Physi- cal Review D, 94(7):076006, October 2016

work page 2016
[39]

On the generalized Friedrichs-Lee model with multiple discrete and continuou s states*

Zhiguang Xiao and Zhi-Y ong Zhou. On the generalized Friedrichs-Lee model with multiple discrete and continuou s states*. Chin. Phys., 49(8):083102, 2025

work page 2025
[40]

Civitarese and M

O. Civitarese and M. Gadella. Physical and mathematica l as- pects of gamow states. Communications on Pure and Applied Mathematics, 396(2):41–113, 2004

work page 2004
[41]

T. D. Lee. Some Special Examples in Renormalizable Fiel d Theory. Phys. Rev., 95:1329–1334, 1954

work page 1954
[42]

K. O. Friedrichs. On the perturbation of continuous spe ctra. Commun. Pure Appl. Math. , 1(4):361–406, 1948

work page 1948
[43]

P Wave Baryons in the Quar k Model

Nathan Isgur and Gabriel Karl. P Wave Baryons in the Quar k Model. Phys. Rev. D, 18:4187, 1978

work page 1978
[44]

Positive Parity Excited Baryons in a Quark Model with Hyperﬁne Interactions

Nathan Isgur and Gabriel Karl. Positive Parity Excited Baryons in a Quark Model with Hyperﬁne Interactions. Phys. Rev. D , 19:2653, 1979

work page 1979
[45]

R. K. Bhaduri, L. E. Cohler, and Y . Nogami. A uniﬁed poten - tial for mesons and baryons. Il Nuovo Cimento A (1965-1970) , 65(3):376–390, 1981

work page 1965
[46]

C. S. Kalman and B. Tran. Baryon spectrum in a potential q uark model. 102(3):835–879

work page
[47]

Ωbaryon spectrum and their decays in a constituent quark model

Ming-Sheng Liu, Kai-Lei Wang, Qi-Fang L¨ u, and Xian-Hu i Zhong. Ωbaryon spectrum and their decays in a constituent quark model. Phys. Rev. D, 101(1):016002, 2020

work page 2020
[48]

Strangeness -2 and -3 baryons in a constituent quark model

Muslema Pervin and Winston Roberts. Strangeness -2 and -3 baryons in a constituent quark model. Phys. Rev. C, 77:025202, 2008

work page 2008
[49]

Roberts and Muslema Pervin

W. Roberts and Muslema Pervin. Heavy baryons in a quark model. Int. J. Mod. Phys. A , 23:2817–2860, 2008

work page 2008
[50]

Hiyama, Y

E. Hiyama, Y . Kino, and M. Kamimura. Gaussian expansion method for few-body systems. Prog. Part. Nucl. Phys., 51:223– 307, 2003

work page 2003
[51]

L. Micu. Decay rates of meson resonances in a quark model . Nucl. Phys. B , 10:521–526, 1969

work page 1969
[52]

Carlitz and M

Robert D. Carlitz and M. Kislinger. Regge amplitude ari sing from su(6)w vertices. Phys. Rev. D, 2:336–342, 1970

work page 1970
[53]

Le Yaouanc, L

A. Le Yaouanc, L. Oliver, O. Pene, and J. C. Raynal. Naive quark pair creation model of strong interaction vertices. Phys. Rev. D, 8:2223–2234, 1973

work page 1973
[54]

Understanding X(3862), X(3872), and X(3930) in a Friedrichs-model-like scheme

Zhi-Y ong Zhou and Zhiguang Xiao. Understanding X(3862), X(3872), and X(3930) in a Friedrichs-model-like scheme. Phys. Rev. D, 96(5):054031, 2017. [Erratum: Phys.Rev.D 96, 099905 (2017)]

work page 2017
[55]

Elementary particle theory of compos ite par- ticles

Steven Weinberg. Elementary particle theory of compos ite par- ticles. Phys. Rev., 130:776–783, 1963

work page 1963
[56]

Zhi-Hui Guo and J. A. Oller. Probabilistic interpretat ion of compositeness relation for resonances. Phys. Rev. D , 93(9):096001, 2016

work page 2016
[57]

V . I. Mokeev and D. S. Carman. Roper Resonance Structure and Exploration of Emergent Hadron Mass from CLAS Elec- troproduction Data. 11 2025

work page 2025
[58]

Origin of res- onances in the chiral unitary approach

Daisuke Jido Tetsuo Hyodo and Atsushi Hosaka. Origin of res- onances in the chiral unitary approach. Prog. Part. Nucl. Phys., 2008

work page 2008
[59]

Norbert Kaiser, P . B. Siegel, and W. Weise. Chiral dynam ics and the S11 (1535) nucleon resonance. Phys. Lett. B , 362:23– 28, 1995. 12

work page 1995
[60]

Nieves and E

J. Nieves and E. Ruiz Arriola. The S(11) - N(1535) and - N(1650) resonances in meson baryon unitarized coupled chan - nel chiral perturbation theory. Phys. Rev. D, 64:116008, 2001

work page 2001
[61]

Bruns, Maxim Mai, and Ulf G

Peter C. Bruns, Maxim Mai, and Ulf G. Meissner. Chiral dy - namics of the S11(1535) and S11(1650) resonances revisited . Phys. Lett. B , 697:254–259, 2011

work page 2011
[62]

Doring and K

M. Doring and K. Nakayama. The Phase and pole structure o f the N*(1535) in pi N — > pi N and gamma N — > pi N. Eur . Phys. J. A, 43:83–105, 2010

work page 2010
[63]

Leinweber, Finn M

Zhan-Wei Liu, Waseem Kamleh, Derek B. Leinweber, Finn M . Stokes, Anthony W. Thomas, and Jia-Jun Wu. Hamiltonian ef- fective ﬁeld theory study of the N∗(1535) resonance in lattice QCD. Phys. Rev. Lett., 116(8):082004, 2016

work page 2016
[64]

Saghai, and Zhenping Li

Jun He, B. Saghai, and Zhenping Li. Study of ηphotoproduc- tion on the proton in a chiral constituent quark approach via one-gluon-exchange model. Phys. Rev. C, 78:035204, 2008

work page 2008
[65]

ηphotoproduction on the quasi-free nucleons in the chiral quark model

Xian-Hui Zhong and Qiang Zhao. ηphotoproduction on the quasi-free nucleons in the chiral quark model. Phys. Rev. C , 84:045207, 2011

work page 2011
[66]

Two-pole structures i n a relativistic Friedrichs–Lee-QPC scheme

Zhi-Y ong Zhou and Zhiguang Xiao. Two-pole structures i n a relativistic Friedrichs–Lee-QPC scheme. Eur . Phys. J. C , 81(6):551, 2021

work page 2021
[67]

E. J. Garzon, J. J. Xie, and E. Oset. Case in favor of the N∗(1700)(3/ 2−). Phys. Rev. C, 87(5):055204, 2013

work page 2013